Abbott's comment came following speculation Austin would become the state's first sanctuary city after the newly elected Democratic sheriff in the county vowed to not cooperate with federal officials on immigration issues, The Blaze reported.

The Republican governor's policy is in line with President-elect Donald Trump's pledge that he would cut off federal funding to sanctuary cities.

Several Democratic mayors and governors have promised to resist the national government by ignoring federal laws and continue protecting illegal immigrants from deportation. These include the mayors of New York, Los Angeles and Chicago, who have vowed their cities will remain places of sanctuary.

Rep. John Culberson, R-Texas, who chairs the House Appropriations subcommittee overseeing the Department of Justice, told Fox News' "American Newsroom" last week: "Using existing law and the power of the purse, I have seen to it that the top 10 sanctuary cities in America have already been certified as violating existing federal law."

Culberson said this means Trump can cut off their money on his first day in the White House, and require some to repay billions of dollars of assistance they have already received, unless they agree to cooperate with immigration officials in upholding the law.